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   <div id="projectname">Parallel Gaussian Process Regression
   &#160;<span id="projectnumber">1.0.0</span>
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   <div id="projectbrief">The implementation of parallel Gaussian process (GP) regression is based on the following publication: Jie Chen, Nannan Cao, Kian Hsiang Low, Ruofei Ouyang, Colin Keng-Yan Tan &amp; Patrick Jaillet. Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations. In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), Bellevue, WA, Jul 11-15, 2013.</div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// Copyright (c) 2014, Jiangbo Yu</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla Public</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// License, v. 2.0. If a copy of the MPL was not distributed with this</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#ifndef PGPR_PARALLEL_H_</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#define PGPR_PARALLEL_H_</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;Eigen/Dense&gt;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &quot;mpi.h&quot;</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__type_8h.html">pgpr_type.h</a>&quot;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__chol_8h.html">pgpr_chol.h</a>&quot;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__cov_8h.html">pgpr_cov.h</a>&quot;</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">using namespace </span>Eigen;</div>
<div class="line"><a name="l00024"></a><span class="lineno"><a class="line" href="classpgpr__parallel.html">   24</a></span>&#160;<span class="keyword">class </span><a class="code" href="classpgpr__parallel.html">pgpr_parallel</a></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;{</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordtype">int</span> rank;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <a class="code" href="classpgpr__parallel.html">pgpr_parallel</a>(<span class="keywordtype">int</span> r):rank(r){}</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordtype">void</span> setRank(<span class="keywordtype">int</span> r){ rank = r;}</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">/* @brief provide the interface to sending message using MPICH</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">     * @param msg row-major matrix-structured message</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">     * @param ori the message tag (the rank of orignation)</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment">     * @param dest the rank of destination </span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keywordtype">void</span> send_msg(<span class="keyword">const</span> Matrix&lt;double, Dynamic, Dynamic, RowMajor&gt; &amp; msg, <span class="keywordtype">int</span> ori, <span class="keywordtype">int</span> dest){</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        <span class="keywordtype">double</span> *sendbuf = NULL;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        MPI_Request send_request;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        MPI_Status status;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordtype">int</span> bufsize;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        <span class="keywordtype">int</span> rows = msg.rows();</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordtype">int</span> cols = msg.cols();</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        bufsize = rows * cols;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        sendbuf = <span class="keyword">new</span>  <span class="keywordtype">double</span>[bufsize];</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="comment">//row-major read row by row</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <span class="keywordtype">int</span> k = 0, i = 0, j = 0;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="keywordflow">for</span>(i = 0; i &lt; rows ; i ++)</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            <span class="keywordflow">for</span>(j = 0; j &lt; cols ; j ++)</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;                sendbuf[k++] = msg(i, j);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        MPI_Isend(sendbuf, bufsize, MPI_DOUBLE, dest, ori, MPI_COMM_WORLD, &amp;send_request);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        MPI_Wait(&amp;send_request, &amp;status);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        <span class="keyword">delete</span> sendbuf;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    }</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keywordtype">void</span> send_msg(<span class="keyword">const</span> MatrixXd &amp;msg, <span class="keywordtype">int</span> ori, <span class="keywordtype">int</span> dest){</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <span class="keywordtype">double</span> *sendbuf = NULL;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        MPI_Request send_request;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        MPI_Status status;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <span class="keywordtype">int</span> bufsize;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keywordtype">int</span> rows = msg.rows();</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="keywordtype">int</span> cols = msg.cols();</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        bufsize = rows * cols;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        sendbuf = <span class="keyword">new</span>  <span class="keywordtype">double</span>[bufsize];</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="comment">//column-major read column by column</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordtype">int</span> k = 0, i = 0, j = 0;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="keywordflow">for</span>(j = 0; j &lt; cols ; j ++)</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            <span class="keywordflow">for</span>(i = 0; i &lt; rows ; i ++)</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                sendbuf[k++] = msg(i, j);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        MPI_Isend(sendbuf, bufsize, MPI_DOUBLE, dest, ori, MPI_COMM_WORLD, &amp;send_request);</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        MPI_Wait(&amp;send_request, &amp;status);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keyword">delete</span> sendbuf;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    }</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="comment">/* @brief receive the message from the machine with rank ori</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment">     * @param msg the column-major matrix where the message would be stored</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">     * @param ori the rank of origination</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">     * @param flag the flag of the message</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keywordtype">void</span> recv_msg(MatrixXd &amp;msg, <span class="keywordtype">int</span> ori, <span class="keywordtype">int</span> flag){</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="keywordtype">double</span> *recvbuf = NULL;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        MPI_Status status;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="keywordtype">int</span> bufsize;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <span class="keywordtype">int</span> rows = msg.rows();</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="keywordtype">int</span> cols = msg.cols();</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        bufsize = rows * cols;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        recvbuf = <span class="keyword">new</span>  <span class="keywordtype">double</span>[bufsize];</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        <span class="comment">//column-major read column by column</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        MPI_Recv(recvbuf, bufsize, MPI_DOUBLE, ori, flag, MPI_COMM_WORLD, &amp;status);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <span class="keywordtype">int</span> k = 0, i = 0, j = 0;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="keywordflow">for</span>(j = 0; j &lt; cols ; j ++)</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            <span class="keywordflow">for</span>(i = 0; i &lt; rows ; i ++)</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;                msg(i, j) = recvbuf[k++];</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keyword">delete</span> recvbuf;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="comment">/* @brief provide the function to do global summary using mapich</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">     * @param map the local matrix</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">     * @param reduce the matrix used to store the result</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment">     * @param op MPICh summary operation </span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment">     * @param dest the machine id where reduced result should be stored, -1 means allreduce</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment">     </span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordtype">void</span> MapReduce(<span class="keyword">const</span> MatrixXd &amp;map, MatrixXd &amp;reduce, MPI_Op op, <span class="keywordtype">int</span> dest){</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        <span class="keywordtype">double</span> *sendbuf = NULL;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        <span class="keywordtype">double</span> *recvbuf = NULL;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="keywordtype">int</span> bufsize;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <span class="keywordtype">int</span> rows = map.rows();</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <span class="keywordtype">int</span> cols = map.cols();</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        bufsize = rows * cols;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        sendbuf = <span class="keyword">new</span>  <span class="keywordtype">double</span>[bufsize];</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;        recvbuf = <span class="keyword">new</span>  <span class="keywordtype">double</span>[bufsize];</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <span class="comment">//column-major read column by column</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <span class="keywordtype">int</span> k = 0, i = 0, j = 0;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="keywordflow">for</span>(j = 0; j &lt; cols ; j ++)</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            <span class="keywordflow">for</span>(i = 0; i &lt; rows ; i ++)</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                sendbuf[k++] = map(i, j);</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        <span class="keywordflow">if</span>(dest == -1)</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            MPI_Allreduce(sendbuf, recvbuf, bufsize, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            MPI_Reduce(sendbuf, recvbuf, bufsize, MPI_DOUBLE, op, dest, MPI_COMM_WORLD);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        <span class="keywordflow">if</span>(dest == -1 || rank == dest){</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            reduce.resize(rows, cols);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;            k = 0;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            <span class="keywordflow">for</span>(j = 0; j &lt; cols ; j ++)</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                <span class="keywordflow">for</span>(i = 0; i &lt; rows ; i ++)</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                    reduce(i, j) = recvbuf[k++];</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        }</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        <span class="keyword">delete</span> sendbuf;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        <span class="keyword">delete</span> recvbuf;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    }</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="comment">/* @brief provide the function to synchronize all the machinese. </span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="keywordtype">void</span> sync(){</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        MPI_Barrier(MPI_COMM_WORLD);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    }</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;};</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="pgpr__chol_8h_html"><div class="ttname"><a href="pgpr__chol_8h.html">pgpr_chol.h</a></div><div class="ttdoc">This file provides Cholesky factorization and some related useful functions such as inverse...</div></div>
<div class="ttc" id="pgpr__type_8h_html"><div class="ttname"><a href="pgpr__type_8h.html">pgpr_type.h</a></div><div class="ttdoc">This file provides important macros, templates, basic data types (e.g., vector, matrix). </div></div>
<div class="ttc" id="pgpr__cov_8h_html"><div class="ttname"><a href="pgpr__cov_8h.html">pgpr_cov.h</a></div><div class="ttdoc">This file provides the covariance class: pgpr_cov, which compute the covariance matrix. </div></div>
<div class="ttc" id="classpgpr__parallel_html"><div class="ttname"><a href="classpgpr__parallel.html">pgpr_parallel</a></div><div class="ttdoc">the class provides the MPICH interface to commmunicate among the machines </div><div class="ttdef"><b>Definition:</b> pgpr_parallel.h:24</div></div>
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